(1) There are 10 beads in a bag: 5 black beads, 3 white beads, and the rest are red. A bead is picked at random. Find the probability that it will be:
a) White
b) Black or red
c) Not white
d) Not blue
Answer (2)
The probability of picking a white bead is 10 3 , while the probability of picking a black or red bead is 10 7 . The probability of not picking a white bead is also 10 7 , and the probability of not picking a blue bead is certain ( 1 ).
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The probability of picking a white bead is calculated by dividing the number of white beads by the total number of beads.
The probability of picking a black or red bead is calculated by dividing the sum of black and red beads by the total number of beads.
Probability of picking a white bead: P ( Whi t e ) = 10 3 .
Probability of picking a black or red bead: P ( Bl a c k or R e d ) = 10 7 .
10 3 and 10 7
Explanation
Understand the problem and provided data We have a bag with 10 beads in total. There are 5 black beads, 3 white beads, and 2 red beads. We want to find the probability of picking a white bead and the probability of picking a black or red bead.
Calculate the probability of picking a white bead (a) To find the probability of picking a white bead, we need to divide the number of white beads by the total number of beads. There are 3 white beads and 10 total beads.
State the probability of picking a white bead The probability of picking a white bead is: P ( Whi t e ) = Total number of beads Number of white beads = 10 3
Calculate the probability of picking a black or red bead (b) To find the probability of picking a black or red bead, we need to add the number of black beads and the number of red beads, and then divide by the total number of beads. There are 5 black beads and 2 red beads.
State the probability of picking a black or red bead The probability of picking a black or red bead is: P ( Bl a c k or R e d ) = Total number of beads Number of black beads + Number of red beads = 10 5 + 2 = 10 7
Final Answer Therefore, the probability of picking a white bead is 10 3 , and the probability of picking a black or red bead is 10 7 .
Examples
Imagine you have a bag of marbles and you want to know the chance of picking a certain color. This is useful in games, experiments, or even in understanding the likelihood of certain events happening in everyday life. For example, if you have a jar with 3 green marbles and 7 blue marbles, the probability of picking a green marble is 10 3 , and the probability of picking a blue marble is 10 7 . These probabilities help you understand the chances of different outcomes.
